Inequalities help!!! (1 Viewer)

billjyang

New Member
Joined
Jul 2, 2017
Messages
2
Gender
Male
HSC
2018
I was wondering how I could do this question:
If (ad+bc)2 <= (a2+b2)(c2+d2),
deduce that:
(a+b)2<= 2(a2+b2)

Now, I know that I am able to do it without the first property given, but the original question is a HENCE question... so i was wondering how to do it using the property above.
I can let c and d = 1, but I am not sure whether you can replace them with integer values.
A worked out solution will help me lots in easing up confusion with inequalities.
THANKS GUYS!!!
 

pikachu975

Premium Member
Joined
May 31, 2015
Messages
2,739
Location
NSW
Gender
Male
HSC
2017
I was wondering how I could do this question:
If (ad+bc)2 <= (a2+b2)(c2+d2),
deduce that:
(a+b)2<= 2(a2+b2)

Now, I know that I am able to do it without the first property given, but the original question is a HENCE question... so i was wondering how to do it using the property above.
I can let c and d = 1, but I am not sure whether you can replace them with integer values.
A worked out solution will help me lots in easing up confusion with inequalities.
THANKS GUYS!!!
Pretty sure you're allowed to since (ad+bc)^2 <= (a^2+b^2)(c^2+d^2) is an identity and hence should work with all a,b,c,d (except restrictions which don't seem to be given) so c =1 and d = 1 should work.
 

fluffchuck

Active Member
Joined
Apr 29, 2016
Messages
239
Location
Sydney
Gender
Male
HSC
2017
The given identity has no restrictions on a,b,c,d except that they all must be real. Letting c=1 and d=1 should be correct
 
Joined
Jun 26, 2016
Messages
57
Gender
Male
HSC
2018
The given identity has no restrictions on a,b,c,d except that they all must be real. Letting c=1 and d=1 should be correct
Bill that question's not gonna appear on our test lmao. Webber told us remember? Only basic identities lmao
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top